Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
444 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#16840654 | C2 | semidirect |
| 3. C2×#16840654 | C2 | semidirect |
| 4. #21460870 | C2 | semidirect |
| 8. #16840661 | C4 | semidirect |
| 27. #14519851 | C2×C4 | semidirect |
| 29. C2×#11758187 | C2×C4 | semidirect |
| 171. C61 | #12609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462063 | 2 |
| C2×#16840654 | 2 |
| #21460870 | 2 |
| #21454248 | 2 |
| #12609 | 61 |